Robotica

Robot Modeling and Control

First Edition

Mark W. Spong, Seth Hutchinson, and M. Vidyasagar

JOHN WILEY & SONS, INC.
New York / Chichester / Weinheim / Brisbane / Singapore / Toronto

Preface

TO APPEAR

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Contents

Preface TABLE OF CONTENTS 1 INTRODUCTION 1.1 Mathematical Modeling of Robots 1.1.1 Symbolic Representation of Robots 1.1.2 The Configuration Space 1.1.3 TheState Space 1.1.4 The Workspace 1.2 Robots as Mechanical Devices 1.2.1 Classification of Robotic Manipulators 1.2.2 Robotic Systems 1.2.3 Accuracy and Repeatability 1.2.4 Wrists and End-Effectors 1.3 Common Kinematic Arrangements of Manipulators 1.3.1 1.3.2 1.3.3 Articulated manipulator (RRR) Spherical Manipulator (RRP) SCARA Manipulator (RRP)

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1.3.4 Cylindrical Manipulator (RPP) 1.3.5 Cartesian manipulator (PPP) 1.3.6 Parallel Manipulator 1.4 Outline of the Text 1.5 Chapter Summary Problems 2

13 14 15 16 24 26

RIGID MOTIONS AND HOMOGENEOUS TRANSFORMATIONS 29 2.1 Representing Positions 30 2.2 Representing Rotations 32 2.2.1 Rotation in the plane 32 2.2.2 Rotations in three dimensions 35 2.3 Rotational Transformations 372.3.1 Similarity Transformations 41 2.4 Composition of Rotations 42 2.4.1 Rotation with respect to the current frame 42 2.4.2 Rotation with respect to the fixed frame 44 2.5 Parameterizations of Rotations 46 2.5.1 Euler Angles 47 2.5.2 Roll, Pitch, Yaw Angles 49 2.5.3 Axis/Angle Representation 50 2.6 Rigid Motions 53 2.7 Homogeneous Transformations 54 2.8 Chapter Summary 57 FORWARD AND INVERSEKINEMATICS 3.1 Kinematic Chains 3.2 Forward Kinematics: The Denavit-Hartenberg Convention 3.2.1 Existence and uniqueness issues 3.2.2 Assigning the coordinate frames 3.2.3 Examples 3.3 Inverse Kinematics 3.3.1 The General Inverse Kinematics Problem 3.3.2 Kinematic Decoupling 3.3.3 Inverse Position: A Geometric Approach 3.3.4 Inverse Orientation 3.3.5 Examples 65 65 68 69 72 75 85 85 87 89 97 98

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3.4 Chapter Summary 3.5 Notes and References Problems 4

100 102 103

VELOCITY KINEMATICS – THE MANIPULATOR JACOBIAN113 4.1 Angular Velocity: The Fixed Axis Case 114 4.2 Skew Symmetric Matrices 115 4.2.1 Properties of Skew Symmetric Matrices 116 4.2.2 The Derivative of a Rotation Matrix 117 4.3 Angular Velocity: The General Case 118 4.4 Addition of Angular Velocities 119 4.5Linear Velocity of a Point Attached to a Moving Frame 121 4.6 Derivation of the Jacobian 122 4.6.1 Angular Velocity 123 4.6.2 Linear Velocity 124 4.6.3 Combining the Angular and Linear Jacobians 126 4.7 Examples 127 4.8 The Analytical Jacobian 131 4.9 Singularities 132 4.9.1 Decoupling of Singularities 133 4.9.2 Wrist Singularities 134 4.9.3 Arm Singularities 134 4.10 Inverse Velocity andAcceleration 139 4.11 Manipulability 141 4.12 Chapter Summary 144 Problems 146 PATH AND TRAJECTORY PLANNING 5.1 The Configuration Space 5.2 Path Planning Using Configuration Space Potential Fields 5.2.1 The Attractive Field 5.2.2 The Repulsive field 5.2.3 Gradient Descent Planning 5.3 Planning Using Workspace Potential Fields 5.3.1 Defining Workspace Potential Fields 149 150 154 154 156 157 158 159

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Mapping workspace forces to joint forces and torques 5.3.3 Motion Planning Algorithm 5.4 Using Random Motions to Escape Local Minima 5.5 Probabilistic Roadmap Methods 5.5.1 Sampling the configuration space 5.5.2 Connecting Pairs of Configurations 5.5.3 Enhancement 5.5.4 Path Smoothing 5.6 trajectory planning 5.6.1 Trajectories for Point to Point Motion 5.6.2 Trajectories for PathsSpecified by Via Points 5.7 Historical Perspective Problems 6 DYNAMICS 6.1 The Euler-Lagrange Equations 6.1.1 One Dimensional System 6.1.2 The General Case 6.2 General Expressions for Kinetic and Potential Energy 6.2.1 The Inertia Tensor 6.2.2 Kinetic Energy for an n-Link Robot 6.2.3 Potential Energy for an n-Link Robot 6.3 Equations of Motion 6.4 Some Common Configurations 6.5 Properties of Robot...